What is the idea of this rook move in this puzzle?

Question

https://www.chess.com/puzzles/problem/1000668

(Also if anyone knows how to start the PGN player with a black move, please let me know)

[Event "Juan Martinez Sola Open A"]
[Site "Almeria ESP"]
[Date "2015.12.18"]
[Round "2.1"]
[White "Arboledas Fernandez,A"]
[Black "Del Rio de Angelis,S"]
[FEN "q3r3/5k2/p4n2/2p1p3/1p3n1Q/1P2N2P/2B3P1/3R3K b - - 1 1"]

1. ... Rh8

My thought process is that the white knight is the only thing preventing Qg2#, so maybe putting a knight on d5 can deflect it away.

The solution of the puzzle for black is Rh8. This puts a threat on the white queen but it can just move away. The engine recommends either 2. Be4 Qxe4 and trade off pieces or 2. Bh7 to sacrifice the bishop, but I don't understand why Black has to trade. So why is Rh8 the correct move?

Answer 1

so maybe putting a knight on d5 can deflect it away

Putting a knight on d5 will close the h1-a8 diagonal after a capture on d5 and therefore gives the chance to counterattack for white. Haven't analyzed but from intuitive POV black might even lose the knight after something like 1. ... N6d5 2. Nxd5 Nxd5 3. Be4

So why is Rh8 the correct move?

Notice the a8 Queen pins the g2 pawn and therefore Rxh3 is a threat. Also White queen doesn't have any good squares apart from e1 and f2 to defend the e3 Knight to the threat of Rxh3 -> Rxe3

My thought process is that the white knight is the only thing preventing Qg2#,

This is exactly the idea behind Rh8 as well. say after Qf2 comes Rxh3, then in the next move comes Rxe3 removing the g2 defending Knight. White queen can't recapture rook since g2 will be unprotected then. This sequence will leave black with an extra piece and with then threats of Re2.

Answer 2

1...Rh8 2. Q-wherever Rxh3+ is winning for Black. The pawn on g2 is pinned and cannot recapture, but after 3.Kg1, Black plays 3...Rxe3 removing the defender of g2 and threatening Qxg2#. White either recaptures and is mated, or is down a decisive amount of material.